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Study of Heat Characteristics of Electroosmotic Mediator and Peristaltic Mechanism via Porous Microtube

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Abstract

Heat characteristics of electroosmotic peristaltic flow are investigated in the porous microtube. Flow and heat equations are modeled using the Jeffrey fluid and viscous dissipation, respectively. The wall is patterned with a periodic array of sinusoidal peristaltic waves. In the presence of axial electric field, the chemical interaction of electrolyte (Jeffrey fluid) and the peristaltic walls (solid) cause an electric double layer at the interface. Based on low Reynolds assumption and Debye-Hückel linearization, the Poisson-Boltzmann equation formally solves the potential distribution, and the resulting non-linear problem is numerically solved via the NDSolve built-in scheme of the computing software Mathematica. Expression of interest like electric potential, velocity, pressure gradient, temperature, streamlines, and wall shear stress are executed numerically within the Jeffrey fluid flow pattern. A complete parametric study is executed to find out the outturn of material parameter λ1, permeability of porous medium K, electroosmotic parameter me, mobility of the medium β, and Brinkman number Br on the thermal features of the flow. This model is also suitable for a wide range of biological microfluidic applications. It is observed that the morphology of heat transfer in the flow is found to be subject to the joint consequence of the geometry of the tube and wall properties. The axial velocity increases monotonically for the Jeffrey fluid when equated to the viscous fluid. Moreover, velocity is noticed to upsurge with higher values of electroosmotic parameter and declines for porous medium and mobility of medium. The magnitude of bolus is larger for the case of Newtonian fluid as compared with non-Newtonian Jeffery fluid. Porosity decays the temperature throughout the microtube. The results presented may potentially be applied to clinical cases associated with the intrapleural membranes, gastrointestinal tract, and capillaries.

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Abbreviations

a :

Tube radius at inlet [L]

b :

Wave amplitude [L]

B r :

Brinkman number

c :

Wave speed [L/T]

c p :

Heat capacity of fluid [ ML2/T2K]

e :

Electron charge [ C]

E z :

Axial electric field [ M/T3A]

E c :

Eckert number

f :

Flow rate [ L3/T]

K :

Permeability parameter

K B :

Boltzmann constant [ML2/T2 K]

k :

Thermal conductivity of fluid [ ML/T3K]

m e :

Electroosmotic parameter

n ± :

Positive, negative ions

n 0 :

Average number of n+ or n− ions

\( \overset{\sim }{p} \) :

Pressure field [ML/T2]

p :

Pressure field

P r :

Prandtl number

R e :

Reynolds number

S c :

Schmidt number

\( \overset{\sim }{t} \) :

Dimensional time [T]

\( \overset{\sim }{T} \) :

Temperature field [K]

U hs :

Helmholtz-Smoluchowski velocity [L/T]

\( \overset{\sim }{U},\overset{\sim }{W} \) :

Dimensional velocity components in stationary frame [L/T]

\( \overset{\sim }{u},\overset{\sim }{w} \) :

Non-dimensional velocity components in wave frame

\( \overset{\sim }{R},\overset{\sim }{Z} \) :

Dimensional coordinates in stationary frame [L]

\( \overset{\sim }{r},\overset{\sim }{z} \) :

Non-dimensional coordinates in wave frame

z v :

Valence of ions

α :

Wave number

β :

Mobility of the medium

∈:

Permittivity of free space [T4A2/ML3]

ε :

Amplitude ratio

θ :

Temperature field [K]

λ :

Wavelength of peristaltic wave [L]

λ D :

Debye length [L]

λ 1 :

Ratio of relaxation to retardation times

λ 2 :

Retardation time [T]

ρ :

Density of fluid [M/L3]

ρ e :

Net ionic charge density [M/L3]

ρc p :

Heat capacity of the fluid [ML2/T2K]

\( \overset{\sim }{\Phi} \) :

Dimensional electric potential distribution [ML2/T2I]

Φ:

Non-dimensional electric potential distribution

ψ :

Dimensional stream function [L2/T]

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, 212013, China

    S. Noreen

  2. Department of Mathematics, COMSATS University Islamabad, Tarlai Kalan, Park Road, Islamabad, 45550, Pakistan

    S. Waheed

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Highlights

Electroosmotically assisted peristaltic flow of the Jeffery fluid through microtube is studied.

Thermal analysis and porosity through peristaltically induced microtube, with applied electric field is also investigated.

The axial velocity increases monotonically for the Jeffery fluid as compared with the Newtonian fluid.

Temperature distribution strongly depends on electroosmotic parameter.

Porosity effect causes the enhancement of wall shear stress.

This analysis is useful in biomedical research.

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Noreen, S., Waheed, S. Study of Heat Characteristics of Electroosmotic Mediator and Peristaltic Mechanism via Porous Microtube. BioNanoSci. 11, 476–488 (2021). https://doi.org/10.1007/s12668-020-00815-0

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